Quantum Numbers: A Skeptic’s Sketch Of Their Development

rep electr

So, I’ve never really accepted that a charged particle moving in a circle must lose energy via radiation. Scientists in the early 20th century who clung to this rule faced mass consternation once they settled on the Nucleus-with-orbiting-Electrons view of the atom. The Electron being the quintessential circulating charged particle, the rule requires that an orbiting Electron should lose energy and spiral into the Nucleus. Instead, physicists such as Niels Bohr were convinced that Electron-orbits were stable. So what did they do?…

Unable to justify these non-deteriorating Electron-orbits, theorists simply… ignored the rule. The thinking was that, since the purported orbits weren’t directly observable anyhow, then insistence upon their existence was merely a solution in search of problem. In other words, it was not necessary to agree that Electrons did or did not move in orbits. In some scenarios, a scientist could think of Electrons as orbiting, in others scenarios, he could just as rightly think of Electrons in some other type of existence. 

In any walk of life, once a person breaks one convention, the ignoring of other conventions becomes easier and easier. It’s getting past that first stigmatization as an outcast that hurts the most. But once you’ve done it and after you’ve found that– hey, you’re still alive, the sun’s still shining, the Earth’s still beneath your feet– then each step away from acceptability is less painful than the one before. 

As Bohr continued working on his model of the atom, he gleefully tossed aside any established theories that got in his way. Ultimately, his model would be, as Arbatzis puts it frankly, “without any mechanical foundation.”  In his physics, Bohr justified the abandonment of, well, physics by stating that there are “many properties of bodies impossible to explain if one assumes” normal mechanistic behavior within the atom. In other words, Bohr was not going to give-in to the Universe– the Universe would have to give-in to Bohr.

Specifically, Bohr was convinced that normal physics would have to be suspended at those times when atoms change from one state to another (for instance, when a “quantum leap” of an Electron is supposed to occur). Arabatzis tells us that Bohr even went so far as introduce a non-mechanical “force” which would govern the interactions inside atoms. He called this (magical?) force, “Zwang.” It would take a couple of years, and the suggestion of “Spin,” before he would let go of this outlandish idea (interestingly, this was just the beginning of new “forces” which physicists would invent ad hoc during the twentieth century to support their theories; come to think of it– Bohr doesn’t get the credit he deserves for this invention– before there was Strong Force, before there was Weak Force– there was Zwang Force!).

Arabatzis informs us that the representation of the Electron was “closely tied” to the “frustrations” of trying to account for the different spectra radiated from atoms when they were energetically excited. These “Spectral Lines” were believed to arise from the Quantum Jumps made by an atom’s Outer Electrons. Physicists were led to the notion of the jumping-bean Electron because of the “sharpness” of the Spectral Lines radiated by the Hydrogen atom. If, instead of jumping, the Electron were to gradually change position, then the frequencies it would radiate would also gradually change.  Instead, what scientists found was that spectral emission patterns shifted suddenly, leaving dark bands between energy-emission frequencies. For each sudden frequency-shift in emissions, the electron was assumed to have “leaped” from one energy level to another.

However, every time the physicists thought they had determined all the possible states of these leaping Electrons, new spectrographic data would come along which was inexplicable by the quantum leap model. The question then arose: if Electron energy-jumps are not behind certain atomic energy-emissions– what IS causing them?

For a long time there was confusion as to how an Electron’s orbit-frequency related to the frequency of energy emitted when the atom radiated. Eventually, Plank’s theory that there was a connection between the “frequency” (orbits-per-time) of Electron revolution and the “frequency” (wave-peaks per time) of atomic radiation had to be abandoned by theorists.

Heisenberg thought he was able to explain one type of the perplexing spectral patterns. When a “doublet” pattern was observed, Heisenberg conjectured that this was caused by the oscillation of the atom’s Core within the internal magnetic field created by the circulating Outer Electron (a magnetic field was, and is, thought by the orthodox to be created by the moving charge of the revolving Electron). When the Core was closer to one side of the Electron’s orbit, then one of the doublet lines would be generated; when it was closer to the other side, the other line would appear.

But as improved instrumentation and technique allowed for the examination of atomic spectral patterns in ever-greater detail, even Quantum Jumps and Core Oscillations were not enough to explain the new complexity emerging. So physicists theorized that Electrons could not only shift from orbits of different distances away from the Core, but they could change the orientations of their orbits (more horizontal or more vertical) around the Core. Both shifts, orbit-distance and orbit-orientation, were thought capable of producing different frequency emissions from the atom. These were the first two “Quantum Numbers” (Electron orbit-distance and orbit-orientation).

However, when analysis of the even more detailed “fine structure” of atomic spectral emissions showed yet more complexity, a third variable– or third “Quantum Number”– was introduced.

The third Quantum Number was perplexing to the physics community. Sommerfeld, its introducer, said that the new variable represented some“hidden rotation” in the atom, and this hidden rotation possessed some “geometric significance” about which “we are quite ignorant.”  The third Quantum Number was called for a time the “Inner Quantum Number.”  Lande interpreted it as the Total Angular Momentum of the atom. Eventually, the Lande view would be rejected, and physicists would come to think of the third Quantum Number as representing the SHAPE of Electron orbits.

Our author informs us that by 1916 there was a growing consensus that spectral emissions could be adequately described by Electron orbit-size, orbit-orientation, and orbit-shape. I’m not sure if Heisenberg’s idea of an oscillating Core had been kicked to the curb or not.

In 1920, when all this still proved insufficient to explain newly arrived data, a fourth Quantum Number was introduced. ,Similar to the initial appearance of the third Quantum Number, what the fourth Quantum Number precisely signified was anybody’s guess. In the beginning, the fourth Quantum Number was interpreted as some collective property of the atom.

However, in 1924, Pauli objected to this interpretation, saying that the only parts of the atom which should be involved in the production of spectral emissions are the Valence, or Outer, Electrons. The rest of the atom, forming the Core, should remain a stable, cohesive unit. Therefore, Quantum Number Four must be a quality specific to the Valence Electron, and according to the math, this fourth number could only have one of two values.  Pauli’s Valence-Electron-specific fourth Quantum Number confused further many already-confused physicists. Bohr, for instance, thought Pauli was introducing a fourth dimension inside the atom for the Electron to move through– and of course, Bohr being Bohr, he was all for it.

A decade earlier, in 1914, William Edward Curtis had pointed out that the formulas which were supposed to predict atomic spectral patterns were actually a little off.  Arabatzis tells us that, in order to combat this discrepancy, Bohr had decided to include in the atomic theory the theory of Relativity.  According to Relativity theory, a fast-moving particle such as the Electron undergoes a contraction in the direction of its motion;  as its velocity increases, its mass will decrease, and vice versa.

Since the Electrons were by then assumed to be travelling in elliptical orbits (contrary to Bohr’s original suggestion of co-axle, circular rings), this meant that their velocities and masses would vary depending on where they were in their orbits (when the orbit is closer to the Core, it was supposed that the Electron would pick-up speed, just as planets do when orbiting the Sun, a.k.a., Kepler’s Second Law). By replacing the values for the Energy and Momentum of the orbiting Electron with values which took into account Relativistic ramifications, Bohr was able to get the answers he wanted from the spectral formulas. How convenient.

As Arabatzis explains it: “by taking into account the relativistic change of the Electron’s mass when it moves within the atom, orbits which had been, from the point of view of classical mechanics, indistinguishable in energy were now assigned slightly different energies. The consequence of that was a multiplication of the energy levels of the Electron within the atom, and therefore of its possible quantum transitions between levels.”

Once Sommerfeld got hold of this idea and started doing the heavy-duty math, he came up with “a proliferation” of Electron energy levels. Now, any observed spectral pattern could be explained with a little Relativity jiggering. But the problem henceforth became one of excess. Paschen found that there were far fewer spectral lines in reality than would be predicted by applying Relativity considerations to Electron orbits.

Before the addition of the Relativity to the atom, the atomic structure was not complex enough to account for the diversity of spectral patterns it emitted; now the atomic structure was too complex– there were too many energy-level options compared to the actual number of patterns being generated.

Sommerfeld tried to implement “selection rules” that would limit the transition-possibilities of Electrons from one orbit to another, but these were never very satisfactory. Of course, he was only doing what physicists had been doing for about two decades now– just coming up with ad hoc patches to fit the most current experimental data.

It was about this time that a few smarties came up with the idea of Electron Spin… but that’s the next post…

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